Question

1) A spring is 17.8 cm long when it is lying on a table. One end is then attached to a hook and the other end is pulled by a force that increases to 28.0 N , causing the spring to stretch to a length of 19.7 cm

a)What is the force constant of this spring?

b)How much work was required to stretch the spring from 17.8 cm to 19.7 cm ?

c)How long will the spring be if the 28.0 N force is replaced by a 56.0 N force?

2)Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.95×10⁶ N , one 15 ∘west of north and the other 15 ∘ east of north, as they pull the tanker 0.84 km toward the north.

-What is the total work they do on the supertanker?

Express your answer with the appropriate units.

3)A bullet is fired into a large stationary absorber and comes to rest. Temperature measurements of the absorber show that the bullet lost 2150 J of kinetic energy, and high-speed photos of the bullet show that it was moving at 980 m/s just as it struck the absorber.

-What is the mass of the bullet?

4)A running house cat has 13.5 J of kinetic energy at speed v.

a)At what speed (in terms of v) will she have 27.0 J of kinetic energy?

Express your answer in terms of v.

b)What would her kinetic energy be if she ran half as fast as the speed in part A?

5)About 50000 years ago, a meteor crashed into the earth near present-day Flagstaff, Arizona. Recent (2005) measurements estimate that this meteor had a mass of about 1.4×108kg (around 150000 tons) and hit the ground at 12 km/s.

a)How much kinetic energy did this meteor deliver to the ground?

Express your answer using two significant figures.

b)How does this energy compare to the energy produced in one day by a standard coal-fired power plant, which generates about 1 billion joules per second?

Express your answer using one significant figure.

6)The food calorie, equal to 4186 J, is a measure of how much energy is released when food is metabolized by the body. A certain brand of fruit-and-cereal bar contains 160 food calories per bar.

a)If a 60.0 kg hiker eats one of these bars, how high a mountain must he climb to "work off" the calories, assuming that all the food energy goes only into increasing gravitational potential energy?

b)If, as is typical, only 23.0 % of the food calories go into mechanical energy, what would be the answer to part (a)? (Note: In this and all other problems, we are assuming that 100 % of the food calories that are eaten are absorbed and used by the body. This is actually not true. A person's "metabolic efficiency" is the percentage of calories eaten that are actually used; the rest are eliminated by the body. Metabolic efficiency varies considerably from person to person.)

7)Tendons are strong elastic fibers that attach muscles to bones. To a reasonable approximation, they obey Hooke's law. In laboratory tests on a particular tendon, it was found that, when a 252 gobject was hung from it, the tendon stretched 1.20 cm .

a)Find the force constant of this tendon in N/m.

b)Because of its thickness, the maximum tension this tendon can support without rupturing is 137 N . By how much can the tendon stretch without rupturing, and how much energy is stored in it at that point?

8)Pebbles of weight w are launched from the edge of a vertical cliff of height h at speed v0. How fast (in terms of the quantities just given) will these pebbles be moving when they reach the ground if they are launched

a)straight up.

b)straight down.

c)horizontally away from the cliff.

d)at an angle θ above the horizontal.

e)How would the answers to the previous parts change if the pebbles weighed twice as much?

9)A 13.0 N package of whole wheat flour is suddenly placed on the pan of a scale such as you find in grocery stores. The pan is supported from below by a vertical spring of force constant 315 N/m .0

-If the pan has negligible weight, find the maximum distance the spring will be compressed if no energy is dissipated by friction.

10)A 15.0 g plastic ball is dropped from a height of 2.90 m and is moving at 2.70 m/s just before it hits the floor.

-How much mechanical energy was lost during the ball's fall?

Answer 1

1) F = Kx

28 = K*(19.7 - 17.8)x10^-2

K = 1473.68/ N/m

b) E = 0.5*Kx^2

E = 0.5*1473.68*[(19.7-17.8)x10^-2]^2

E = 0.266 J

c) F = Kx

56 =1473.68*x

x = 0.038 m = 3.8 cm

d = 17.8+3.8 = 21.6 cm

2) W = F*s*cos(theta)

W = 1.95x10^6*0.84x10^3*cos15

W = 1.58x10^9 N

3) E = 0.5*mv^2

2150 = 0.5*m*980^2

m = 0.004477 Kg

m = 4.477 g

4) KE1/KE2 = 0.5*mv1^2/0.5*mv2^2

13.5/27 = v^2/v2^2

v2^2 = 2*v^2

v2 = v*sqrt(2)

6) E = mgh

160*4186 = 60*9.8*h

h = 1139.04 m

b) 0.23*E = mgh

0.23*160*4186 = 60*9.8*h

h = 261.98 m

7) mg = Kx

0.252*9.8 = K*1.2x10^-3

K = 2058 N/m

b) F = Kx

137 = 2058*x

x = 0.0665 m

x = 6.657 cm

E = 0.5*Kx^2

E = 0.5*2058*0.06657^2

E = 4.56 J

8) When launchd vertically up , the object thrown has same speed when reaches the same point from where it is thrown

v^2 - u^2 = 2gh

v^2 = vo^2+2gh

v = sqrt(vo^2+2gh)

b) v^2 - u^2 = 2gh

v^2 = vo^2+2gh

v = sqrt(vo^2+2gh)

c) thrown horizontally

v = sqrt(2gh)

d) v^2 - u^2 = 2gh

v^2 = [vosin(theta)]^2+2gh

v = sqrt[ (vo*sin(theta))^2+2gh]

e) the gravity affect on the object is not dependent on mass so it doesnot change

9) W = Kx

13 = 315*x

x = 0.04127 m

x = 4.127 cm

10) loss of energy = initial energy - final energy

loss = mgh - 0.5*mv^2

loss = 15x10^-3(9.8*2.9 - 0.5*2.7^2)

loss = 0.3716 J